In the restricted one-way communication model [1]}, [2]}, [3]},
the \(i\) -th player sends exactly one message to the \((i+1)\) -st player for \(i\in [t-1]\)  following \(\Pi _t\) ,
and then \(P_t\)  announces the output of \(\Pi _t\)  as specified by \(\Pi _{out}\) .
Note that in this setting there are only \(k-1\)  messages sent by \(P_1,\dots , P_{k-1}\) , and we do not count the final output announced by \(P_t\)  in the communication in order to best correspond to streaming algorithms.
This is also known as a sententious protocol in previous work, e.g., [4]}.
We denote the \(t\) -player one-way communication complexities of \(f\) by \(\overrightarrow{\mathbf {DCC}}_t(f)\)  and \(\overrightarrow{\mathbf {RCC}}_{t,\error }(f)\) , respectively.
